A method for the study of fully developed parallel flow in straight ducts of arbitrary cross section

AbstractA method is presented for the study of fully developed parallel flow of Newtonian viscous fluid in uniform straight ducts of very general cross-section. The method is based upon the concept of contour lines of constant velocity in a typical cross section of the duct, and uses the function which describes the contour lines as an independent variable to derive the integral momentum equation. The resulting ordinary integro-differential equation is, in principle, much easier to solve than the original momentum equation in partial differential equation form. Several illustrative examples of practical interest are included to explain the method of solution. Some of these solutions are compared with available solutions in the literature. All details are explained by graphs and tables. The method has several interesting features. The study has relevance to biomedical engineering research for blood and urinary tract flow.

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Bars under Torsional Loading: A Generalized Beam Theory Approach

ISRN Civil Engineering ◽

10.1155/2013/916581 ◽

2013 ◽

Vol 2013 ◽

pp. 1-39 ◽

Cited By ~ 8

Author(s):

Evangelos J. Sapountzakis

Keyword(s):

Cross Section ◽

Practical Interest ◽

Beam Theory ◽

Arbitrary Cross Section ◽

Shear Stresses ◽

Theory Approach ◽

3D Fem ◽

Mass Model ◽

Dynamic Analyses ◽

Load Vector

In this paper both the static and dynamic analyses of the geometrically linear or nonlinear, elastic or elastoplastic nonuniform torsion problems of bars of constant or variable arbitrary cross section are presented together with the corresponding research efforts and the conclusions drawn from examined cases with great practical interest. In the presented analyses, the bar is subjected to arbitrarily distributed or concentrated twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. For the dynamic problems, a distributed mass model system is employed taking into account the warping inertia. The analysis of the aforementioned problems is complete by presenting the evaluation of the torsion and warping constants of the bar, its displacement field, its stress resultants together with the torsional shear stresses and the warping normal and shear stresses at any internal point of the bar. Moreover, the construction of the stiffness matrix and the corresponding nodal load vector of a bar of arbitrary cross section taking into account warping effects are presented for the development of a beam element for static and dynamic analyses. Having in mind the disadvantages of the 3D FEM solutions, the importance of the presented beamlike analyses becomes more evident.

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The longitudinal-transverse bending of reinforced concrete rods

MATEC Web of Conferences ◽

10.1051/matecconf/201819601038 ◽

2018 ◽

Vol 196 ◽

pp. 01038 ◽

Cited By ~ 1

Author(s):

Yury Nemirovskii ◽

Sergey Tikhonov

Keyword(s):

Reinforced Concrete ◽

Cross Section ◽

Limit State ◽

Arbitrary Cross Section ◽

Bending Moments ◽

Maximum Deformation ◽

Limit Value ◽

Transverse Bending ◽

Method Of Solution ◽

Conditional Limit

The longitudinal transverse bending of multilayer rods made of reinforced concrete of arbitrary cross-section is considered. It is assumed that the coefficients in the connection equation between stresses, strains and temperature are different in each layer. The achievement of maximum deformation of the permissible limit value at stretching or compression is accepted as the criterion of conditional limit state in the i-layer. The case of longitudinal-transverse bending of a hinged rod is considered as an example of this method of solution. The distribution of bending moments and longitudinal forces, displacements and deformations is determined.

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